Abstract
In this paper we propose and analyze a class of simple Nyström discretizations of the hypersingular integral equation for the Helmholtz problem on domains of the plane with smooth parametrizable boundary. The method depends on a parameter (related to the staggering of two underlying grids) and we show that two choices of this parameter produce convergent methods of order two, while all other stable methods provide methods of order one. Convergence is shown for the density (in uniform norm) and for the potential postprocessing of the solution. Some numerical experiments are given to illustrate the performance of the method.
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Communicated by: I. Graham
VD is partially supported by MICINN Project MTM2010-21037. FJS is partially supported by NSF grant DMS 1216356
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Domínguez, V., Lu, S.L. & Sayas, F. A Nyström method for the two dimensional Helmholtz hypersingular equation. Adv Comput Math 40, 1121–1157 (2014). https://doi.org/10.1007/s10444-014-9344-5
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DOI: https://doi.org/10.1007/s10444-014-9344-5